A330652 Decimal expansion of (phi^phi - 1/phi)/2, where phi = (1 + sqrt(5))/2 = A001622.

7, 8, 0, 2, 1, 1, 7, 8, 9, 5, 9, 3, 8, 5, 2, 1, 4, 9, 5, 8, 3, 9, 7, 9, 4, 3, 4, 2, 5, 2, 8, 0, 3, 8, 6, 7, 0, 4, 3, 3, 6, 7, 0, 6, 0, 9, 4, 3, 7, 4, 5, 8, 7, 4, 6, 0, 6, 1, 6, 6, 6, 5, 0, 6, 7, 1, 0, 8, 9, 9, 9, 3, 3, 5, 6, 9, 6, 1, 8, 7, 6, 1, 9, 9, 9, 0, 4, 7, 7, 8, 5, 0, 4, 1, 3, 9, 7, 2, 5, 0, 8

Offset

1,1

Comments

Conjecture: (phi^phi - 1/phi)/2 = integral_{x=0..oo} exp(-x*(2 + phi)) * (cosh(x) + sqrt(5) * sinh(x))^phi dx.

Links

Table of n, a(n) for n=1..101.

Alexander R. Povolotsky, Interesting Integral, post in newsgroup sci.math.research, April 04, 2017.

Example

0.78021178959385214958397943425280386704336706094374587460616665067108999335696...

Mathematica

RealDigits[(GoldenRatio^GoldenRatio - 1/GoldenRatio)/2, 10, 120][[1]]

Prog

(Magma) (((Sqrt(5)+1)/2)^((Sqrt(5)+1)/2) - 1/((Sqrt(5)+1)/2))/2

Crossrefs

Cf. A001622 (golden ratio phi).

Sequence in context: A221114 A198841 A332634 * A181438 A333972 A088396

Adjacent sequences: A330649 A330650 A330651 * A330653 A330654 A330655

Keyword

nonn,cons

Author

Vincenzo Librandi, Dec 29 2019

Status

approved